We introduce a new mode of operation for CD-systems of restarting automata
by providing explicit enable and disable conditions in the form of regular
constraints. We show that, for each CD-system M of restarting automata and
each mode m of operation considered by Messerschmidt and Otto, there exists
a CD-system M' of restarting automata of the same type as M that, working in
the new mode ed, accepts the language that M accepts in mode m. Further, we
prove that in mode ed, a locally deterministic CD-system of restarting automata of type RR(W)(W) can be simulated by a locally deterministic CD-system of restarting automata of the more restricted type R(W)(W). This is the first time that a non-monotone type of R-automaton without auxiliary symbols is shown to be as expressive as the corresponding type of RR-automaton.